Counting Fractions on a Number Line
Count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines.
Read this first
A fraction is a number. It has its own place on the number line.
The line from 0 to 1 is cut into 4 equal steps. Each step is one quarter.
Words you need
- Numerator
- The top number. It counts the pieces.
- Denominator
- The bottom number. It says how many pieces make one whole.
- Mixed numeral
- A whole number and a fraction together, like 1 and a half.
Worked example
e.g. Where does 3/4 sit on the number line?
- The bottom number is 4. So cut 0 to 1 into 4 equal steps.
- The top number is 3. So count 3 steps from 0.
- Stop at the third mark. That is 3/4.
- 3/4 sits three steps along, just before 1.
Bottom number tells you how many steps. Top number tells you how far to count.
Practice
The pictures fade as you go. By the last few you are on your own.
1Where does 1/2 sit?with a picture
AnswerExactly in the middle of 0 and 1.
2Where does 2/5 sit?with a picture
AnswerTwo steps along out of five.
3Count on in quarters from 0. Say the first five.with a hint
Need a hint?
Keep the bottom number the same.
Answer0, 1/4, 2/4, 3/4, 1.
4What comes after 1 and 1/4 if you count in quarters?with a hint
Need a hint?
Add one more quarter.
Answer1 and 2/4.
5Is 5/4 more or less than 1?on your own
AnswerMore. 4/4 makes 1, so 5/4 is past it.
6Write 6/4 as a mixed numeral.on your own
Answer1 and 2/4.
7Which is closer to 1: 3/4 or 5/4?on your own
AnswerThey are the same distance away, one quarter.
Think about it
1
Why is a fraction a number and not just a picture?
One good answerIt has a place on the number line, the same as 3 or 7.
2
What does 4/4 equal?
One good answerOne whole. All four steps have been counted.
Common mistakes
Thinking a bigger bottom number means a bigger fraction.
More steps means smaller steps. 1/8 is smaller than 1/4.
Counting the marks instead of the steps.
Start counting steps from 0, not from the first mark.